Electrical Energy Consumption in Tunisia

Data Set of electrical energy consumption in Tunisia:

The data set includes observations of electrical energy consumption registred for every day of the month during 7 years (2010-2017).

it includes:

• annee (Year)
• mois (Month)
• jour (Day)
• type (Mixed variable resuming year-month-day)
• tmin (Minimum temperature)
• Tmax (Maximum temperature)
• Tmoy (The average temperature)
• Energie_trans (Consumed electrical energy)
• JF (Holiday)
• Ramadhan
• Janvier-December (From January to December)
• Lundi-Dimanche (From monday to sunday)
• Date

Packages needed:

library(shiny)
library(plotly)
library(shinydashboard)
library(DT)
library(plotly)
library(caret)
library(dygraphs)
library(xts)         
library(tidyverse)
library(lubridate)
library(forecast)
library(ggplot2)
library(plotly)
library(ggcorrplot)
library(RColorBrewer)
library(readxl)

D=read_excel('donnees_Electricite.xlsx',sheet = 2)
datatable(D, rownames = 1, filter="top", options = list(pageLength = 5, scrollX=T) )

The time series component:

Date=paste(D$annee,D$mois,D$jour,sep = '-')
D$Date=as.Date(Date)
Variab<- ts(D$Energie_trans,start = c(2010, as.numeric(format(D$Date[1], "%j"))),
              frequency = 365)
  
  don <- xts(x =Variab, order.by = D$Date)
  
  dygraph(don) %>%
    dyOptions(labelsUTC = TRUE, fillGraph=TRUE, fillAlpha=0.1, drawGrid = FALSE, colors="#D8AE5A") %>%
    dyRangeSelector() %>%
    dyCrosshair(direction = "vertical") %>%
    dyHighlight(highlightCircleSize = 5, highlightSeriesBackgroundAlpha = 0.2, hideOnMouseOut = FALSE)  %>%
    dyRoller(rollPeriod = 1)

It can be seen that the consumption of electrical energy has an ascending trend.

  decompose(Variab,type="multiplicative") %>% autoplot+theme_bw()+ggtitle("Seasonal Decomposition of Electrical Energy Consumption")

From the plots above we can recongnize an ascending trend and a stationary remainder (noise).

As the time series increases in magnitude, the seasonal variation increases as well. It’s why we should use a multiplicative model.

Correlation between Variables:

Tmoy, tmin and Tmax are considered explicative variables, the choice of which one to include in the model is based on its correlation with the energy consumption. Statistically, we can’t include two correlated explicative variables in the same model.

  ggcorrplot(cor(D[,c(8,5:7)]),
             outline.col = "white",
             lab = TRUE,
             lab_size = 5,
             lab_col = '#736F6E',
             ggtheme = ggplot2::theme_gray,
             colors = c('#595959', "white", "#6D9EC1"))

In the following, tmin is considered the optimal variable to use among tmin, Tmax and Tmoy with a correlation with Energy equal to 0.65.

Modeling of the time series:

tslm function is used to explicate the consumption of electrical energy using various explicative variables:

train <- D[1:2557, ] #excluding the last year to predict energy consumption later
test <-  D[2558:2922, ]

train=ts(train,start = c(2010, as.numeric(format(train$Date[1], "%j"))),frequency = 365)

fit <- tslm(Energie_trans ~annee+tmin+JF+Ramadhan+Janvier+
Fevrier+Mars+Avril+Mai+Juin+Juillet+Aout+Septembre+Octobre+Novembre+Lundi+Mardi+Mercredi+Jeudi+Vendredi+Samedi, data = train)
summary(fit)

## 
## Call:
## tslm(formula = Energie_trans ~ annee + tmin + JF + Ramadhan + 
##     Janvier + Fevrier + Mars + Avril + Mai + Juin + Juillet + 
##     Aout + Septembre + Octobre + Novembre + Lundi + Mardi + Mercredi + 
##     Jeudi + Vendredi + Samedi, data = train)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -23000.4  -2241.9    -74.7   2079.2  18662.4 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.229e+06  8.535e+04 -49.552  < 2e-16 ***
## annee        2.128e+03  4.240e+01  50.195  < 2e-16 ***
## tmin         3.812e+02  3.157e+01  12.073  < 2e-16 ***
## JF          -5.907e+03  4.391e+02 -13.451  < 2e-16 ***
## Ramadhan     6.790e+02  3.610e+02   1.881   0.0601 .  
## Janvier     -8.135e+02  4.133e+02  -1.968   0.0492 *  
## Fevrier     -8.642e+01  4.245e+02  -0.204   0.8387    
## Mars        -3.011e+03  4.118e+02  -7.312 3.52e-13 ***
## Avril       -4.693e+03  4.248e+02 -11.046  < 2e-16 ***
## Mai         -2.455e+03  4.419e+02  -5.556 3.04e-08 ***
## Juin         4.258e+03  5.000e+02   8.516  < 2e-16 ***
## Juillet      1.396e+04  5.741e+02  24.321  < 2e-16 ***
## Aout         1.437e+04  5.823e+02  24.681  < 2e-16 ***
## Septembre    5.096e+03  5.422e+02   9.400  < 2e-16 ***
## Octobre     -2.153e+03  4.848e+02  -4.442 9.31e-06 ***
## Novembre    -4.499e+03  4.318e+02 -10.419  < 2e-16 ***
## Lundi        6.858e+03  3.171e+02  21.627  < 2e-16 ***
## Mardi        8.192e+03  3.171e+02  25.838  < 2e-16 ***
## Mercredi     8.340e+03  3.171e+02  26.306  < 2e-16 ***
## Jeudi        8.438e+03  3.171e+02  26.614  < 2e-16 ***
## Vendredi     8.226e+03  3.168e+02  25.963  < 2e-16 ***
## Samedi       5.158e+03  3.171e+02  16.266  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4286 on 2535 degrees of freedom
## Multiple R-squared:  0.833,  Adjusted R-squared:  0.8317 
## F-statistic: 602.3 on 21 and 2535 DF,  p-value: < 2.2e-16

accuracy(fit)

##                        ME     RMSE     MAE        MPE     MAPE      MASE
## Training set 1.615193e-13 4267.356 3046.05 -0.3339313 4.319366 0.5606067
##                   ACF1
## Training set 0.7842202

This model reflects 83.27% of the reality (Adjusted R-squared=0.8317).

Forecasting :

The model previously constructed will be used to make a forecast of one year of electrical energy in Tunisia.

  fore<-forecast(fit,test)
    p=plot_ly() %>%
      add_lines(x = (D)$Date , y = (D)$Energie_trans,
                color = I('#595959') , name = "observed") %>%
      add_ribbons(x = (test)$Date, ymin = fore$lower[, 2], ymax = fore$upper[, 2],
                  color = I("#b3b3ff"), name = "95% CI") %>%
      add_lines(x = (test)$Date, y = fore$mean, color = I("#0073e6"), name = "prediction")
  p

The forecasted values of consumed electrical energy is accurate as we can observe through the plot.

Electrical energy consumption will continue to have an increasing trend through time.

Bibliography:

• Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. J. (1990). STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6(1), 3–33. http://bit.ly/stl1990

• Rob J Hyndman and George Athanasopoulos, Monash University, Australia. Forecasting: Principles and Practice. https://otexts.com/fpp2/

• Yan Holtz.the R graph gallery. https://www.r-graph-gallery.com/index.html